Prove that sin A1-cos A-1-cos Asin A-2 A

L.H.S =sinA1+cosA+1+cosAsinA =sin^2A+(1+cosA)^2sinA(1+cosA) =sin^2A+1+cos^2A+2cosAsinA(1+cosA) =sin^2A+cos^2A+1+2cosAsinA(1+cosA) =1+1+2 ...

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Monotonically Increasing Functions

Prove that ...

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Prove that $\frac{sin A}{1 + cos A} + \frac{1 + cos A}{sin A} = 2 csc A$

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\frac{sin A - cos A}{sin A + cos A} = tan 2 A - sec 2 A

\frac{s i n A + c o s A}{s i n A - c o s A} + \frac{s i n A - c o s A}{s i n A + c o s A} = \frac{2}{s i n^{2} A - c o s^{2} A} = \frac{2}{2 s i n^{2} A - 1} = \frac{2}{1 - 2 c o s^{2} A}

\frac{cos A}{1 + sin A} + \frac{1 + sin A}{cos A} = 2 sec A

\frac{1 + cos A + sin A}{1 + cos A - sin A} = \frac{1 + sinA}{cos A}

\frac{cos A + sin A - 1}{cos A - sin A + 1} = \frac{1}{cosec A + cot A}

{cosec}^{2} A - {cot}^{2} A = 1.

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